Substitute Barry Conlon's dramatic strike five minutes from time was enough to earn Bradford a 1-0 win and end Bury's unbeaten away record.
The match appeared to be heading for a draw until Bradford captain Graeme Lee hammered a 30-yard free-kick against the crossbar and Conlon out-jumped goalkeeper Wayne Brown to head the rebound into the net.
Earlier, on-loan midfielder Nicky Law had missed Bradford's best chance when he scuffed wide after Omar Daley's cross had been turned into his path with 28 minutes gone.
Bury's best two efforts came in the second half, but Bradford keeper Rhys Evans turned Efe Sodje's header over the bar and then saved leading-scorer Andy Bishop's shot at the second attempt.
Football Results
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